SOME GENERALIZATIONS OF MULTIPLE LAGUERRE POLYNOMIALS VIA RODRIGUES FORMULA

Abstract

This paper aims to provide systematic investigation of the family of polynomials generated by the Rodrigues' formulas K-n1,K- n2 ((alpha 1, alpha 2))(x, k, p) = (-1)(n1+n2)e(pxk) [Pi(2)(j=1)x(-alpha j) d(n)j/dx(n)j x(alpha j +nj)]e(-pxk), and M-n1,M- n2 ((alpha 0,p1, .p2)) (x, k) = (-1)(n1+n2)/p(1)(n1)p(2)(n2)x - alpha(0) [Pi(2)(j=1) d(pjxk) d(n)j/dx(n)j e(-pjxk)] x(n1+n2+alpha 0), which include the multiple Laguerre I and the multiple Laguerre II polynomials, respectively. The explicit forms, certain operational formulas involving these polynomials with some applications and linear generating functions for K-n1,K-n2 ((alpha 1, alpha 2))(x, k, p) and M-n1, n2((alpha 0, p1, .p2))(x, k) are obtained.